Three triangles have the side lengths given below: Triangle X: 8cm, 13cm, 5cm
Triangle Y: 14cm, 30cm, 17cm
Triangle Z: 26cm, 10cm, 24cm

Which of the triangles could not be right triangles?

Triangle Z

Step-by-step explanation:

If a triangle is a right angle triangle, it will follow the Pythagoras theorem.

By Pythagoras theorem,

(Hypotenuse)² = (Leg 1)² + (Leg 2)²

Options (1)

Side lengths of the triangle X: 8 cm, 13 cm, 5 cm

By Pythagoras theorem,

(13)² = 8² + 5²

169 = 64 + 25

169 = 69

False.

Option (2)

Side lengths of triangle Y: 14 cm, 30 cm, 17 cm

By Pythagoras theorem,

(30)² = (14)² + (13)²

900 = 196 + 169

900 = 365

False.

Option (3)

Side lengths of triangle Z: 26 cm, 10 cm, 24 cm

By Pythagoras theorem,

(26)² = (10)² + (24)²

676 = 100 + 576

676 = 676

True.

Therefore, triangle Z represents a right triangle.

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